Study of Characteristics of the Radio-Frequency Sheath over a Substrate with a Circular Trench

Since processed substrates usually exhibit nonplanar surface structures in Micro-Electro-Mechanical-Systems (MEMS) etching, a two-dimensional (2D) fluid model is developed to simulate the characteristics of the sheath near a conductive substrate with a circular trench, which is placed in an argon discharge powered by a radio-frequency (rf) current source. The model consists of 2D time-dependent fluid equations, the Poisson equation, and a current balance equation that can self-consistently determine the instantaneous voltage on the substrate placed on a powered electrode. The effects of both the aspect ratio (depth/width) and the structure of the trench on the characteristics of the sheath are simulated. The time-averaged potential and electric field in the sheath are calculated and compared for different discharge parameters. The results show that the radial sheath profile is not uniform and always tends to adapt to the contour of the substrate, which is believed to be the moulding effect. Affected by the structure of the substrate surface, the potential and electric field near the inner and outer sidewalls of the trench exhibit obvious non-uniformity, which will inevitably lead to non-uniformity in etching, such as notching. Furthermore, with a fixed amplitude of the rf current source, the potential drops and the sheath thickness decrease with an increase in aspect ratio.     

Modeling of magnetized collisional plasma sheath with nonextensive electron distribution and ionization source

The properties of an atmospheric-pressure collisional plasma sheath with nonextensively distributed electrons and hypothetical ionization source terms are studied in this work. The Bohm criterion for the magnetized plasma is extended in the presence of an ion–neutral collisional force and ionization source. The effects of electron nonextensive distribution, ionization frequency, ion– neutral collision, magnetic field angle and ion temperature on the Bohm criterion of the plasma sheath are numerically analyzed. The fluid equations are solved numerically in the plasma–wall transition region using a modified Bohm criterion as the boundary condition. The plasma sheath properties such as charged particle density, floating sheath potential and thickness are thoroughly investigated under different kinds of ion source terms, contributions of collisions, and magnetic fields. The results show that the effect of the ion source term on the properties of atmosphericpressure collisional plasma sheath is significant. As the ionization frequency increases, the Mach number of the Bohm criterion decreases and the range of possible values narrows. When the ion source is considered, the space charge density increases, the sheath potential drops more rapidly, and the sheath thickness becomes narrower. In addition, ion–neutral collision, magnetic field angle and ion temperature also significantly affect the sheath potential profile and sheath thickness.     

Collisional Sheath in the Electronegative Radio-Frequency Plasma

A model of collisional RF sheath with negative ions is discussed in this paper. The influences of collision and negative ions on the parameters of the sheath are studied through numerical simulation. It is found that when the collision coefficient increases and the RF power is fixed, the electrode potential and sheath electric field potential increase, the electrode current and thickness of the sheath decrease. When the negative ion content changes, the same phenomenon Occurs,     

The Effect of Gas Flow Rate on Radio-Frequency Hollow Cathode Discharge Characteristics

It is known that gas flow rate is a key factor in controlling industrial plasma processing. In this paper, a 2D PIC/MCC model is developed for an rf hollow cathode discharge with an axial nitrogen gas flow. The effects of the gas flow rate on the plasma parameters are calculated and the results show that： with an increasing flow rate, the total ion（N＋2, N＋） density decreases, the mean sheath thickness becomes wider, the radial electric field in the sheath and the axial electric field show an increase, and the energies of both kinds of nitrogen ions increase;and, as the axial ion current density that is moving toward the ground electrode increases, the ion current density near the ground electrode increases. The simulation results will provide a useful reference for plasma jet technology involving rf hollow cathode discharges in N2.     

Two-dimensional self-consistent numerical simulation of the whole discharge region in an atmospheric argon arc

A 2D self-consistent numerical model of the whole argon-arc discharge region that includes electrodes is developed in this work to facilitate analysis of the physical processes occurring in atmospheric arc plasma. The 2D arc column model contains the ionization and thermal non-equilibrium, which is coupled with a 1D electrode sheath model. The influence of plasma-species diffusion near the electrode region is investigated based on Maxwell–Stefan equations and the generalized Ohm's law. The numerical results of argon free-burning arcs at atmospheric pressure are then investigated. The simulation shows that the plasma is obviously in the state of thermal and ionization equilibrium in the arc core region, while it deviates from thermal and ionization equilibrium in the arc fringe region. The actual electron density decreases rapidly in the near-anode and near-cathode regions due to non-equilibrium ionization, resulting in a large electron number gradient in these regions. The results indicate that electron diffusion has an important role in the near-cathode and near-anode regions. When the anode arc root gradually contracts, it is easy to obtain a positive voltage drop of the anode sheath (I = 50 A), while it remains difficult to acquire a positive anode sheath voltage drop (I = 150 A). The current–voltage characteristics predicted by our model are found to be identical to the experimental values.     

Frequency Matching Effects on Characteristics of Bulk Plasmas and Sheaths for Dual-Frequency Capacitively Coupled Argon Discharges： One-Dimensional Fluid Simulation

A one-dimensional fluid model is proposed to simulate the dual-frequency capacitively coupled plasma for Ar discharges. The influences of the low frequency on the plasma density, electron temperature, sheath voltage drop, and ion energy distribution at the powered electrode are investigated. The decoupling effect of the two radio-frequency sources on the plasma parameters, especially in the sheath region, is discussed in detail.     

Ar射频放电特性随时间演化的PIC/MCC模拟

采用等离子体粒子模拟方法(PIC/MCC)方法对一维模型模拟了容性耦合等离子体(CCP)源放电过程中等离子体的动力学行为。在模拟氩气放电的过程中,综合考虑了电子与Ar之间的弹性碰撞、激发、电离以及Ar与Ar+之间的弹性碰撞和电荷交换过程。由模拟结果可知,射频极板附近鞘层区域在极短时间内形成,其厚度随着时间的增加而增厚;而射频极板处的粒子通量随着时间的增加逐渐减小。经过一段时间后,射频极板处平均粒子通量、平均电流以及鞘层平均厚度逐渐趋于平衡。在鞘层区域电流主要由位移电流构成,在等离子体区域电流主要由传导电流贡献。最后讨论了达到平衡态后等离子体密度、电势、电场强度和能量的空间分布情况。     

Characteristics of Positive Ions in the Sheath Region of Magnetized Collisional Electronegative Discharges

A hydrodynamic model is used to investigate the characteristics of positive ions in the sheath region of a low-pressure magnetized electronegative discharge. Positive ions are modeled as a cold fluid, while the electron and negative ion density distributions obey the Boltzmann distribution with two different temperatures. By taking into account the ion-neutral collision effect in the sheath region and assuming that the momentum transfer cross section has a power law dependence on the velocity of positive ions, the sheath formation criterion （modified Bohm＇s criterion） is derived and it is shown that there are specified maximum and minimum limits for the ion Mach number M. Considering these two limits of M, the behaviors of electrostatic potential, charged particle density distributions and positive ion velocities in the sheath region are studied for different values of ion-neutral collision frequency.     

Experimental study of a low-pressure hybrid RF discharge

Experimental study of the low-pressure hybrid RF discharge with both inductive and capacitive channels was carried out. The RF power unit consists of inductor(antenna) and capacitor plates connected in parallel to the same RF power source. A separating capacitor Csepis included into the circuit between the antenna ends and the lead connected to the discharge capacitor plate in order to prevent the closing of the capacitive circuit through direct current by inductor and to control the contribution of capacitive channel to discharge sustaining. It is shown that at low power of the RF power source, power coupling to the discharge mainly occurs through the capacitive channel. Increasing the power of the RF power source increases the power coupled in the inductive channel, electron density, and current flowing through the capacitive channel. This leads to increasing voltage drop on the separating capacitor and partial cutoff of the capacitive channel. At separating capacitance values below certain value(below 50 pF in the present experiments), the self-bias of the loaded plate of the discharge capacitor becomes positive indicating that the thickness of the electrode sheath of the loaded electrode decreases compared to thickness of the sheath of the grounded electrode. The thickness of the space-charge sheath of the grounded electrode decreases with increasing power coupled to the plasma. At separating capacitance below 50 pF, higher harmonics of the RF voltage and current are actively generated in the capacitive discharge channel. Increasing the separating capacitance leads to decreasing electron density, increasing effective electron temperature and more effective RF energy coupling to plasma due to increasing relative importance of the capacitive discharge channel.     

Surface Potential of Dust Grains at the Sheath Edge of Electronegative Dusty Plasmas

In this paper we investigate the dust surface potential at the sheath edge of electronegative dusty plasmas theoretically, using the standard fluid model for the sheath and treating electrons and negative ions as Boltzmann particles but positive ions and dust grains as cold fluids. The dust charging model is self-consistently coupled with the sheath formation criterion by the dust surface potential and the ion Mach number, moreover the dust density variation is taken into account. The numerical results reveal that the dust number density and negative ion number density as well as its temperature can significantly affect the dust surface potential at the sheath edge.     

Combined Effect of Ion Temperature and Magnetic Field on Collisionless Sheath Structure

A steady state two-fluid model has been used to study the characteristics of the collisionless plasma sheath in the presence of an external magnetic field and by taking into account both the ion temperature and the ion drift velocity at the sheath edge. The number and momentum equations of ions, the Boltzmann distribution of electrons and Poisson equations are solved numerically. The dependence of the Bohm magnetized sheath criterion to ion temperature is examined. It is shown that the ion temperature has significant effects on the sheath characteristics such as ion velocity, charged particles densities and electric potential. In the specific orientations of the magnetic field, it is found that by increasing the ion temperature, the ions do not achieve energy and the kinetic energy of the ions in the depth direction reaches the specific value at bigger distance from the plasma-sheath boundary.     

Theoretical Study on the Characteristics of Atmospheric Radio Frequency Discharges by Altering Electrode Gap

In this paper, we present a theoretical study on the discharge characteristics of radio-frequency discharges at atmospheric pressure driven by a higher frequency of 40.68 MHz while the electrode gap is altered. Based on the analytical equations and simulation data from a one-dimensional fluid model, an optimal gap between electrodes, at which the largest electron density is obtained, can be observed under a constant power condition; however, as the electrode gap increases the time-averaged electron temperature decreases, and the underpinning physics is also discussed based on the simulation results. This study indicates that at a constant power by choosing an appropriate electrode spacing, the rf discharge can be effectively optimized at atmospheric pressure.     

The Electrostatic Cylindrical Sheath in a Plasma

The electrostatic sheath with a cylindrical geometry in an ion-electron plasma is investigated. Assuming a Boltzmann response to electrons and cold ions with bulk flow, it is shown that the radius of the cylindrical geometry do not affect the sheath potential significantly. We also found that the sheath potential profile is steeper in the cylindrical sheath compared to the slab sheath. The distinct feature of the cylindrical sheath is that the ion density distribution is not monotonous. The sheath region can be divided into three regions, two ascendant regions and one descendant region.     

On the electron sheath theory and its applications in plasma–surface interactions

In this work, an improved understanding of electron sheath theory is provided using both fluid and kinetic approaches while elaborating on their implications for plasma–surface interactions. A fluid model is proposed considering the electron presheath structure, avoiding the singularity in electron sheath Child–Langmuir law which overestimates the sheath potential. Subsequently, a kinetic model of electron sheath is established, showing considerably different sheath profiles in respect to the fluid model due to non-Maxwellian electron velocity distribution function and finite ion temperature. The kinetic model is then further generalized and involves a more realistic truncated ion velocity distribution function. It is demonstrated that such a distribution function yields a super-thermal electron sheath whose entering velocity at the sheath edge is greater than the Bohm criterion prediction. Furthermore, an attempt is made to describe the electron presheath–sheath coupling within the kinetic framework, showing a necessary compromise between a realistic sheath entrance and the inclusion of kinetic effects. Finally, the secondary electron emissions induced by sheath-accelerated plasma electrons in an electron sheath are analysed and the influence of backscattering is discussed.     

A Multi-Scale Study on Silicon-Oxide Etching Processes in C4F8/Ar Plasmas

A multi-scale numerical method coupled with the reactor,sheath and trench model is constructed to simulate dry etching of SiO_2 in inductively coupled C_4F_8 plasmas.Firstly,ion and neutral particle densities in the reactor are decided using the CFD-ACE+ commercial software.Then,the ion energy and angular distributions(IEDs and IADs) are obtained in the sheath model with the sheath boundary conditions provided with CFD-ACE+.Finally,the trench profile evolution is simulated in the trench model.What we principally focus on is the effects of the discharge parameters on the etching results.It is found that the discharge parameters,including discharge pressure,radio-frequency(rf) power,gas mixture ratios,bias voltage and frequency,have synergistic effects on IEDs and IADs on the etched material surface,thus further affecting the trench profiles evolution.     

Ion Temperature Effect on Weakly Collisional DC Plasma Sheath

Using a collisional two-fluid model, we investigate the ion temperature effect on the sheath formation criterion as well as the sheath structure in electropositive plasmas. In this work, temperature dependence of the characteristics of a weakly collisional DC plasma sheath is examined numerically. It will be shown in the constant cathode electric potential, the more the ion temperature, the low the thickness of sheath. Moreover, for a special set of physical parameters, the sheath formation criterion is not fulfilled for ion temperature under a minimum value.     

Sheath Structures of Strongly Electronegative Plasmas

The sheath structures of strongly electronegative plasmas axe investigated on basis of the accurate Bohm criterion obtained by Sagdeev potential. It is found that the presheath transition between the bulk plasma and the sheath almost does not exist there, and that distributions of electrons, negative and positive ions in the sheath form a pure positive ion sheath near the boundary of the electrode. Furthermore, the density distribution of space net charge has a peak near the sheath edge, the spatial potential within the sheath falls faster, and the sheath thickness becomes thinner.     

Study on the characteristics of non-Maxwellian magnetized sheath in Hall thruster acceleration region

The secondary electron emission (SEE) and inclined magnetic field are typical features at the channel wall of the Hall thruster acceleration region (AR), and the characteristics of the magnetized sheath have a significant effect on the radial potential distribution, ion radial acceleration and wall erosion. In this work, the magnetohydrodynamics model is used to study the characteristics of the magnetized sheath with SEE in the AR of Hall thruster. The electrons are assumed to obey non-extensive distribution, the ions and secondary electrons are magnetized. Based on the Sagdeev potential, the modified Bohm criterion is derived, and the influences of the non-extensive parameter and magnetic field on the AR sheath structure and parameters are discussed. Results show that, with the decrease of the parameter q, the high-energy electron leads to an increase of the potential drop in the sheath, and the sheath thickness expands accordingly, the kinetic energy rises when ions reach the wall, which can aggravate the wall erosion. Increasing the magnetic field inclination angle in the AR of the Hall thruster, the Lorenz force along the $x$ direction acting as a resistance decelerating ions becomes larger which can reduce the wall erosion, while the strength of magnetic field in the AR has little effect on Bohm criterion and wall potential. The propellant type also has a certain effect on the values of wall potential, secondary electron number density and sheath thickness.     

Investigation of nanosecond-pulsed dielectric barrier discharge actuators with powered electrodes of different exposures

Nanosecond-pulsed dielectric barrier discharge actuators with powered electrodes of different exposures were investigated numerically by using a newly proposed plasma kinetic model. The governing equations include the coupled continuity plasma discharge equation, drift-diffusion equation, electron energy equation, Poisson's equation, and the Navier–Stokes equations.Powered electrodes of three different exposures were simulated to understand the effect of surface exposure on plasma discharge and surrounding flow field. Our study showed that the fully exposed powered electrode resulted in earlier reduced electric field breakdown and more intensive discharge characteristics than partially exposed and rounded-exposed ones. Our study also showed that the reduced electric field and heat release concentrated near the right upper tip of the powered electrode. The fully exposed electrode also led to stronger shock wave, higher heating temperature, and larger heated area.     

Effects of Magnetic Field and Ion Velocity on SPT Plasma Sheath Characteristics

The distribution of magnetic field in Hall thruster channel has significant effect on its discharge process and wall plasma sheath characteristics. By creating physical models for the wall sheath region and adopting two-dimensional particle in cell simulation method, this work aims to investigate the effects of magnitude and direction of magnetic field and ion velocity on the plasma sheath characteristics. The simulation results show that magnetic field magnitudes have small impact on the sheath potential and the secondary electron emission coefficient, magnetic azimuth between the magnetic field direction and the channel radial direction is proportional to the absolute value of the sheath potential, but inversely proportional to the secondary electron emission coefficient. With the increase of the ion incident velocity, secondary electron emission coefficient is enhanced, however, electron density number, sheath potential and radial electric field are decreased. When the boundary condition is determined, with an increase of the sinmlation area radial scale, the sheath potential oscillation is aggravated, and the stability of the sheath is reduced.